SOLUTION: You have a ball in the shape of a sphere, with a diameter of 10cm. You want to fill the ball with a gel liquid. You use a cone to fill the sphere. The cone has a height of 3cm and

Algebra ->  Volume -> SOLUTION: You have a ball in the shape of a sphere, with a diameter of 10cm. You want to fill the ball with a gel liquid. You use a cone to fill the sphere. The cone has a height of 3cm and       Log On


   

Question 1064720: You have a ball in the shape of a sphere, with a diameter of 10cm. You want to fill the ball with a gel liquid. You use a cone to fill the sphere. The cone has a height of 3cm and an unknown radius. What will the radius need to be to fill the ball completely with one pour from the cone? Show your work.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of the sphere
%284%2F3%29pi%2A%2810%2F2%29%5E3

%284%2F3%29pi%2A%285%5E3%29

%28500pi%29%2F3



Cone volume needs to be the same as for the sphere.
r is radius of this cone's circular base.
%281%2F3%29%2A3%2Api%2Ar%5E2=500pi%2F3

pi%2Ar%5E2=500pi%2F3

r%5E2=500%2F3

highlight%28r=10%2Asqrt%285%2F3%29%29
(or you could continue and rationalize the denominator.)